Apart from fuel gauge related problems, one problem our DA-40 had was with the various engine-related switches that are on the top left of the panel. They are very exposed with the hood open, as you enter or leave the aircraft. Apparently one of the switches (I think the flimsy FADEC Auto/B switch) had taken a hit from somebodys foot or so, and caused both FADECs to reset simultaneously, continuously. Pilot was in the circuit as this happened and able to make a safe landing. Since then, the club has put guards on each of these switches so it's virtually impossible to hit the switch themselves by accident, as you climb aboard.
Other than that, and the fuel gauge related problems, I've never heard of anything out of the ordinary with our DA-40. But I've only been flying this one since January.
I, for one, have no problem flying a DA-40 over the Channel.